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Simple difference quotient question. Function -> simplify answer

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Simple difference quotient question. Function --> simplify answer

Homework Statement



I just don't understand this question! Here, I will take a picture of it. Can someone please explain how I answer these? Or even show me a website that shows how to do these? Its not in my review book.

QUESTION is in ATTACHMENTS!

Homework Equations





The Attempt at a Solution

 

Attachments

Answers and Replies

  • #2
vela
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It seems pretty straightforward what the question is asking. What specifically don't you understand?
 
  • #3
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Can you tell me the first step? When you look at this, what is the first thing you see/do?
 
  • #4
vela
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Exactly what the problem statement says: evaluate the difference quotient. If you don't understand what that means, try looking up "difference quotient" in your book.
 
  • #5
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Must be missing something here.

I would plug in the f(x) values to the 2nd function, but there is no x's, just h ? How do I plug in values?
 
  • #6
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The problem is asking you to evaluate the difference quotient to find f'(3).
 
  • #7
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wow I'm lost. :(
 
  • #8
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Dude, f(x) = f(3+h) if x = 3+h
 
  • #9
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wow I'm lost. :(
The difference quotient to find the derivative of a function, f'(x), looks like this:

$$ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$

The difference quotient to find the derivative of a function at a specific number a, f'(a), looks like this:

$$ f'(a) = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$$

Do you recognize that your problem is asking for f'(3)?
 
  • #10
SammyS
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Homework Statement



I just don't understand this question! Here, I will take a picture of it. Can someone please explain how I answer these? Or even show me a website that shows how to do these? Its not in my review book.
Here's the image:

attachment.php?attachmentid=50253&d=1346172108.jpg

***************************

So, if [itex]f(x)=4+3x-x^2\,,[/itex] then what is [itex]f(3+h)\ ?[/itex]
 
  • #11
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Here's the image:

attachment.php?attachmentid=50253&d=1346172108.jpg

***************************

So, if [itex]f(x)=4+3x-x^2\,,[/itex] then what is [itex]f(3+h)\ ?[/itex]
SammyS, that is the one part I am having trouble fully understanding....
 
  • #12
vela
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It would have helped if you could have said that right from the beginning.

In f(x)=4+3x-x2, the x is what's called a dummy variable. Anything you put in the lefthand side where the x is shows up wherever the x appears on the righthand side. For example, suppose you have g(x) = 2x+4. Then
\begin{align*}
g(y) = 2y+4 \\
g(h+3) = 2(h+3)+4 \\
g(4z) = 2(4z)+4 \\
g(weasel) = 2(weasel)+4 \\
g(3) = 2(3)+4 = 10
\end{align*}
Now tell us what you think f(3+h) is equal to in your problem.
 
  • #13
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SammyS, that is the one part I am having trouble fully understanding....
Apparently you don't understand how to evaluate a function's formula.

If g(t) = 3 - t2 (for example)
then g(1) = 3 - (1)2 = 3 - 1 = 2
and g(5) = 3 - (5)2 = 3 - 25 = -23
and g(a + 2) = 3 - (a + 2)2

So for your function, what is f(3 + h)?
 
  • #14
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"So for your function, what is f(3 + h)?"

f(3+h) = 4 + 3(3+h) - (3+h)^2 ?
 
  • #15
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Yes. You'll need to expand the right side and collect common terms.
 
  • #16
vela
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Yup, that's it.
 

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